Broyden–Fletcher–Goldfarb–Shanno algorithm

Summary

Broyden–Fletcher–Goldfarb–Shanno algorithm is an algorithm^[1]. It draws 237 Wikipedia views per month (algorithm category, ranking #43 of 337).^[2]

Key Facts

• Broyden–Fletcher–Goldfarb–Shanno algorithm is credited with the discovery of Charles George Broyden^[3].
• Broyden–Fletcher–Goldfarb–Shanno algorithm is credited with the discovery of Roger Fletcher^[4].
• Broyden–Fletcher–Goldfarb–Shanno algorithm is credited with the discovery of Donald Goldfarb^[5].
• Broyden–Fletcher–Goldfarb–Shanno algorithm is credited with the discovery of David Shanno^[6].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's instance of is recorded as algorithm^[7].
• Charles George Broyden is named after Broyden–Fletcher–Goldfarb–Shanno algorithm^[8].
• Roger Fletcher is named after Broyden–Fletcher–Goldfarb–Shanno algorithm^[9].
• Donald Goldfarb is named after Broyden–Fletcher–Goldfarb–Shanno algorithm^[10].
• David Shanno is named after Broyden–Fletcher–Goldfarb–Shanno algorithm^[11].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's subclass of is recorded as Quasi-Newton method^[12].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's part of is recorded as nonlinear programming^[13].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's Freebase ID is recorded as /m/066pcg^[14].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's computes solution to is recorded as optimization problem^[15].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's defining formula is recorded as \begin{aligned}\bf p_k&=-B_k^{-1}\nabla\bf f_k\ \alpha_k&=\arg\min f(\bf x_k+\alpha \bf p_k)\ \bf s_k& =\alpha_k\bf p_k\ \bf x_{k+1}&=\bf x_k+\bf s_k\ \bf y_{k+1}&=\nabla\bf f_{k+1}-\nabla\bf f_k\B_{k+1}&=B_k+\frac{\bf y_k\bf y_k^\top}{\bf y_k^\top\bf s_k}-\frac{B_k{\bf s}_k{\bf s}_k^\top B_k^\top}{{\bf s}_k^\top B_k{\bf s}_k}\end{aligned}^[16].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's BabelNet ID is recorded as 17280119n^[17].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's maintained by WikiProject is recorded as WikiProject Mathematics^[18].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's Microsoft Academic ID is recorded as 132721684^[19].
• Broyden–Fletcher–Goldfarb–Shanno algorithm's OpenAlex ID is recorded as C132721684^[20].

Body

Geography

Broyden–Fletcher–Goldfarb–Shanno algorithm's part of is recorded as nonlinear programming^[13].

Designation and Status

Broyden–Fletcher–Goldfarb–Shanno algorithm's instance of is recorded as algorithm^[7].

History and Context

Things named after include Charles George Broyden^[8], a mathematician^[21], 1933–2011^[22], of United Kingdom^[23]; Roger Fletcher^[9], a mathematician^[24], 1939–2016^[25], of United Kingdom^[26], awarded the The George B. Dantzig Prize^[27], specialised in mathematics^[28]; Donald Goldfarb^[10], a mathematician^[29], b. 1941^[30], of United States^[31]; and David Shanno^[11], a mathematician^[32], 1938–2019^[33], of United States^[34].

Why It Matters

Broyden–Fletcher–Goldfarb–Shanno algorithm draws 237 Wikipedia views per month (algorithm category, ranking #43 of 337).^[2] It has Wikipedia articles in 8 language editions, a strong signal of global cultural recognition.^[35] It is known by 5 alternative names across languages and contexts.^[36]